Equatorial stability analysis of dust particle orbits within a charged rotating disc of dust

Abstract

Stability of circular orbits of the dust particles within a charged rotating disc of dust with respect to perturbations in the equatorial plane is analyzed. Within Einstein-Maxwell theory, the charged rotating disc of dust is an axisymmetric, stationary solution given in terms of a post-Newtonian expansion. The disc solution is characterized by a rigid rotation around the axis of symmetry and a constant specific charge $\epsilon$. It is found that for $\epsilon<1$ all realized dust particle orbits are stable and for $\epsilon=1$ all dust particles are in marginally stable states.